Making a copy of a website with wget should work like that:

wget -r mywebsite.com

-r recursively crawls the site, default is until level 5.

With filenames with non-latin characters, wget is not happy:

bash Incomplete or invalid multibyte sequence encountered Incomplete or invalid multibyte sequence encountered Incomplete or invalid multibyte sequence encountered Incomplete or invalid multibyte sequence encountered

That seems to be a bug in wget.

Workaround

wget -r --restrict-file-names=nocontrol mywebsite.com